You can't set default values in an interface, but you can accomplish what you want to do by using Optional Properties (compare paragraph #3):

Simply change the interface to:

interface IX {
    a: string,
    b?: any,
    c?: AnotherType
}

You can then do:

let x: IX = {
    a: 'abc'
}

And use your init function to assign default values to x.b and x.c if those properies are not set.

While @Timar's answer works perfectly for null default values (what was asked for), here another easy solution which allows other default values: Define an option interface as well as an according constant containing the defaults; in the constructor use the spread operator to set the options member variable

interface IXOptions {
    a?: string,
    b?: any,
    c?: number
}

const XDefaults: IXOptions = {
    a: "default",
    b: null,
    c: 1
}

export class ClassX {
    private options: IXOptions;

    constructor(XOptions: IXOptions) {
        this.options = { ...XDefaults, ...XOptions };
    }

    public printOptions(): void {
        console.log(this.options.a);
        console.log(this.options.b);
        console.log(this.options.c);
    }
}

Now you can use the class like this:

const x = new ClassX({ a: "set" });
x.printOptions();

Output:

set
null
1

You can implement the interface with a class, then you can deal with initializing the members in the constructor:

class IXClass implements IX {
    a: string;
    b: any;
    c: AnotherType;

    constructor(obj: IX);
    constructor(a: string, b: any, c: AnotherType);
    constructor() {
        if (arguments.length == 1) {
            this.a = arguments[0].a;
            this.b = arguments[0].b;
            this.c = arguments[0].c;
        } else {
            this.a = arguments[0];
            this.b = arguments[1];
            this.c = arguments[2];
        }
    }
}

Another approach is to use a factory function:

function ixFactory(a: string, b: any, c: AnotherType): IX {
    return {
        a: a,
        b: b,
        c: c
    }
}

Then you can simply:

var ix: IX = null;
...

ix = new IXClass(...);
// or
ix = ixFactory(...);

You can use the Partial mapped type as explained in the documentation:

In your example, you'll have:

interface IX {
    a: string;
    b: any;
    c: AnotherType;
}

let x: Partial<IX> = {
    a: 'abc'
}

I use the following pattern:

Create utility type Defaults<T>:

type OptionalKeys<T> = { [K in keyof T]-?: {} extends Pick<T, K> ? K : never }[keyof T];
type Defaults<T> = Required<Pick<T, OptionalKeys<T>>>

Declare class with options/defaults:

// options passed to class constructor
export interface Options {
    a: string,
    b?: any,
    c?: number
}

// defaults
const defaults: Defaults<Options> = {
    b: null,
    c: 1
};

export class MyClass {
    // all options in class must have values
    options: Required<Options>;

    constructor(options: Options) {
        // merge passed options and defaults
        this.options = Object.assign({}, defaults, options);
    }
}

Create class instance:

const myClass = new MyClass({
    a: 'hello',
    b: true,
});

console.log(myClass.options);
// { a: 'hello', b: true, c: 1 }

Default values to an interface are not possible because interfaces only exists at compile time.

Alternative solution:

You could use a factory method for this which returns an object which implements the XI interface.